Scientific Notation

How to write in scientific notation.

Move the decimal…

until it is on the right side of the first nonzero number.

Example: 123 000 000 000The decimal will be between 1 & 2

1.23 000 000 000

Drop non significant zeros.

• 123 000 000 000 has 3 significan digits, therefore the zeros are not significant therefore you may drop these.

• Therefore, 1.23 000 000 becomes 1.23

Find the exponent.

• Count how many places you moved the decimal point.

• This will be your exponent.• If you do not see a decimal point, assume it is

at the end of the number• In the number 123 000 000 000. you will need

to move the decimal point 11 places to get it between 1 & 2.

Put it all together.

• 123 000 000 000 = 1.23 x 1011

Always use the power of 10.

Follow the same steps for small numbers

Example: 0.00000123Move decimal point = 0000001.23Drop non significant zeros = 1.23Count number of places moved = 6Add a negative to the exponent = -6Final answer: 1.23 x 10-6

Practice Problems

I. Writing in scientific notationa. 20 000 Hz = 2 x 104 Hzb. 105 000 g = 1.05 x 105 gc. 0.005 cm/h = 5 x 10-3 cm/hd. 0.02 cm/s = 2 x 10-2 cm/se. 160 050 000 km = 1.6005 x 108 kmf. 0.000003050 kg = 3.050 x 10-6 kg

Practice Problems

• Write the following numbers in standard notation.a. 1.47 x 103 m/s = 1470 m/sb. 1 x 10-8 mm = .00000001 mmc. 2.5 x 100 N = 2.5